CDD precoding for open loop SU MIMO

ABSTRACT

A method for data transmission is provided that includes selecting a codeword from a predetermined codebook based on a transmission rank, generating a precoding matrix based on the selected codeword, precoding a plurality of symbols with the precoding matrix, and transmitting the precoded symbols.

CLAIM OF PRIORITY

This application makes reference to, incorporates the same herein, andclaims all benefits accruing under 35 U.S.C. §119 from applicationsearlier filed in the U.S. Patent & Trademark Office on 8 Jun. 2007 andthere duly assigned Ser. No. 60/929,027, and on 28 Jun. 2007 and thereduly assigned Ser. No. 60/929,455, respectively.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method and to a circuit fortransmitting data in a communication system, and more specifically, tomore reliable and efficient methods and circuits for selecting precodingmatrix for the open-loop structures.

2. Description of the Related Art

Orthogonal Frequency Division Multiplexing (OFDM) is a popular wirelesscommunication technology used to multiplex data in the frequency. Thetotal bandwidth in an OFDM system is divided into narrowband frequencyunits called subcarriers. In frequency-selective multi-user scheduling,a contiguous set of subcarriers potentially experiencing upfadedistortion is allocated for transmission to a user. Infrequency-diversity transmission, however, the allocated subcarriers arepreferably uniformly distributed over the whole spectrum.

In a wireless mobile system employing OFDM based access, the overallsystem performance and efficiency can be improved by using, in additionto time-domain scheduling, frequency-selective multi-user scheduling. Ina time-varying frequency-selective mobile wireless channel, it is alsopossible to improve the reliability of the channel by spreading and/orcoding the information over the subcarriers.

A multiple antenna communication system, which is often referred to as amultiple input multiple output (MIMO) system, is widely used incombination with OFDM technology, in a wireless communication system toimprove system performance. MIMO schemes use multiple transmittingantennas and multiple receiving antennas to improve the capacity andreliability of a wireless communication channel.

A popular MIMO scheme is MIMO precoding. With preceding, the datastreams to be transmitted are precoded, i.e., pre-multiplied by aprecoding matrix, before being passed on to the multiple transmittingantennas in a transmitter. In a pre-coded MIMO system, inverseoperations are performed at the receiver to recover the transmittedsymbols. The received symbols are multiplied with the inverse precodingmatrices.

Recent efforts of the precoding approach were applied to both transmitdiversity and MIMO spatial multiplexing. A composite precoder isconstructed based on a unitary precoder such as Fourier matrix precodermultiplied with another unitary precoder representing a transmitdiversity scheme such as Cyclic Delay Diversity (CDD). It should benoted that the principles of the current disclosure also apply to thecases of non-unitary precoding or unitary precoders other than Fouriermatrix precoder. Matrix D is introduced as a symbol for a CDD precodingmatrix and Matrix P is introduced as a symbol for a Discrete Fouriertransform (DFT) matrix, then the combined matrix C=DP becomes a columnpermutation on alternative subcarriers. Efforts have been made toimprove precoding methods in both of open loop structures and closedloop structures in following 3rd Generation Partnership Project (3GPPTM) documents:

3GPP RAN1 contribution R1-072461, “High Delay CDD in Rank AdaptedSpatial Multiplexing Mode for LTE DL”, May 2007, Kobe, Japan;

3GPP RAN1 contribution R1-072019, “CDD precoding for 4 Tx antennas”, May2007, Kobe, Japan;

3GPP RAN1 contribution R1-072633, “Updated T536.211 v1.1.0”, May 2007,Kobe, Japan; and

3 GPP 36211-110: “3 GPP TS 36.211 v1.0.0 3rd Generation PartnershipProject; Technical Specification Group Radio Access Network; PhysicalChannels and Modulation Release 8”, March 2007.

In an alternative preceding CDD structure, a large-delay CDD is appliedin conjunction with the precoding matric, if a feedback of PrecodingMatrix Indication (PMI) is available. For Large-delay CDD with PMIfeedback, the codebook shall be selected from the Single User MIMO(SU-MIMO) codebook or a subset thereof. For large-delay CDD, precedingfor spatial multiplexing shall be done according to the followingequation:y(k)=W(k)QD(k)Ps(k),  (1)

where the preceding matrix W(k) is the channel-dependent defaultprecoding (sub)matrix which is selected from a codebook of size Nt×p.Note that k is the subcarrier index, Nt is the number of antenna portsin transmitter and p is the transmission rank. The matrices P, and D(k)are of size p×p, while W(k) is Nt×p. The choice of Q can be of severaldifferent forms. Q=I where I is p×p identity matrix (in this case Q canbe removed); or Q=P⁻¹ which is the inverse of P.

In the contemporary methods for obtaining W(k), it is assumed that thechoice of W(k) is chosen according the PMI, which is obtained fromuplink feedback. Once a PMI is obtained for a subband, the same choiceof W(k) is applied throughout this subband. That is, W(k) stays the samewithin the same subband. However, in the high speed scenarios the PMIfeedback is not reliable and the PMI in the feedback cannot be used. Thehigh speed system may be defined as an open-loop system. It is thereforenot clear how the precoder W(k) should be selected in an open-loopsystem. Furthermore, the prior methods have no solution for the caseswhere no PMI is available for the less than full rank case.

SUMMARY OF THE INVENTION

It is, therefore, an object of the present invention to provide animproved method and an improved circuit for high speed, open-loopprecoding.

It is another object to provide reliable circuit and more reliablemethods of selecting W(k) for high-speed open-loop precoding CDD, forvarious antenna correlation configurations.

In one embodiment of the current invention, the precoding matrix W(k) isselected according to a feedback without precoding matrix index (PMI) inthe uplink for each given User Equipment (UE), and this feedback withoutprecoding matrix index (PMI) is different from the dynamic PMI. The sameW(k) is applied to the given UE across the scheduled subband. Thismethod is especially useful in the configuration where the Node-Bantennas are highly correlated. “Node-B” antenna contains transmitter(s)and receiver(s) employed for communicating directly with the mobiledevices in a radio frequency.

The Selection of W(k) Based on SU-MIMO Codebook

In another embodiment of the current invention, the SU-MIMO codebook isdenoted as C_(U)(p), for a given transmission rank p that may be 1, 2, 3or 4. The size of the codebook for rank p is denoted by N_(p). Thecodewords c_(i)(p) are denoted in codebook C_(U)(p)={c₁(p), . . . ,c_(N) _(p) (p)} i=1, . . . , N_(p). Note that c_(i)(p) is a Nt×p matrix.

Furthermore, one way of selecting the precoding matrix W(k) for rank pis to cycle through the codebook C_(U)(p) as k increases. There are twooptions of how fast the precoding matrix changes. In the first option,the precoding matrix W(k) changes every p subcarriers within thesubband. In the second option, the precoding matrix W(k) changes everysubcarrier within the subband.

In another embodiment of this invention, for each codebook C_(U)(p), thesubsets C_(U,S)(p)⊂C_(U)(p) are defined, such thatC_(U,S)(p)={c_(s,1)(p), . . . , C_(s,J) _(p) (P)} while J_(p) is thesize of the subset (J_(p) is less than or equal to N_(p)).

Furthermore, one way of selecting the precoding matrix for W(k) is topick a subset C_(U,S)(p) for a given rank p, and then cycle through thissubset as k increases. There are two options of how fast the precodingmatrix changes. In the first option, the precoding matrix W(k) changesevery p subcarriers within the subband. In the second option, theprecoding matrix W(k) changes every subcarrier within the subband.

In another embodiment of the invention, W(k) is selected as one of thesubmatrices in the set C_(U)(p), for a given rank p. And the W(k) isfixed for all the subcarriers in the subband scheduled for the UE.

The Selection of W(k) Based on DFT Submatrix

In another embodiment of the current invention, a selection of W(k) isbased on DFT submatrix. A 4Tx DFT matrix is defined as:

$\begin{matrix}\begin{matrix}{F = \lbrack \begin{matrix}f_{1} & f_{2} & f_{3} &  f_{4} \rbrack\end{matrix} } \\{{= {0.5*\begin{bmatrix}1 & 1 & 1 & 1 \\1 & j & {- 1} & {- j} \\1 & {- 1} & 1 & {- 1} \\1 & {- j} & {- 1} & j\end{bmatrix}}},}\end{matrix} & (2)\end{matrix}$where f_(i), i=1, . . . , 4 is the i'th column of the above DFT matrix.The set of rank dependent sub-matrices C_(F)(p) is dependent on thetransmission rank p:

$\begin{matrix}\begin{matrix}{{C_{F}(2)} = \{ {{c_{1}(2)},{c_{2}(2)},...\mspace{14mu},{c_{6}(2)}} \}} \\{= \{ \begin{matrix}{\lbrack {f_{1},f_{2}} \rbrack,} & {\lbrack {f_{2},f_{3}} \rbrack,} & {\lbrack {f_{3},f_{4\;}} \rbrack,}\end{matrix} } \\{ \begin{matrix}{\lbrack {f_{4},f_{1}} \rbrack,} & {\lbrack {f_{1},f_{4}} \rbrack,} & \lbrack {f_{2},f_{4}} \rbrack\end{matrix} \}.}\end{matrix} & (3) \\\begin{matrix}{{C_{F}(3)} = \{ {{c_{1}(3)},{c_{2}(3)},...\mspace{14mu},{c_{6}(3)}} \}} \\{= \begin{matrix}\{ \lbrack f_{1}   & f_{2} & { f_{3} \rbrack,} & \lbrack f_{2}  & f_{3} & { f_{4} \rbrack,}\end{matrix}} \\{ \begin{matrix}\lbrack f_{3}  & f_{4} & { f_{1} \rbrack,} & \lbrack f_{4}  & f_{1} &  f_{2} \rbrack\end{matrix} \}.}\end{matrix} & (4) \\\begin{matrix}{{C_{F}(4)} = \{ {c_{1}(4)} \}} \\{= {\{ \lbrack {{f_{1\;,}f_{2}},f_{3},f_{4}} \rbrack \}.}}\end{matrix} & (5)\end{matrix}$

For each set C_(F)(p), subsets C_(F,S)(p)⊂C_(F)(p) are defined, suchthat C_(F,S)(p)={c_(s,1)(p), . . . , c_(s,J) _(p) (p)} and J_(p) is thesize of the subset (J_(p) is less than or equal to the size ofC_(F)(p)).

Furthermore, one way of selecting the preceding matrix for W(k) is topick a subset C_(F,S)(p) for a given rank p, and then cycle through thissubset as k increases. There are two options of how fast the precedingmatrix changes. In the first option, the precoding matrix W(k) changesevery p subcarriers within the subband. In the second option, thepreceding matrix W(k) changes every subcarrier within the subband.

In another embodiment of the invention, W(k) is selected as one of thesubmatrices in the set C_(F)(p), for a given rank p. And the W(k) isfixed for all the subcarriers in the subband scheduled for the UE.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the invention and many of the attendantadvantages thereof, will be readily apparent as the same becomes betterunderstood by reference to the following detailed description whenconsidered in conjunction with the accompanying drawings in which likereference symbols indicate the same or similar components, wherein:

FIG. 1 is an illustration of a simplified example of data transmissionand reception using Orthogonal Frequency Division Multiplexing (OFDM);

FIG. 2A is a two coordinate illustration of contiguous, or localizedsubcarrier allocation for frequency-selective multi-user scheduling andfrequency diversity in OFDM;

FIG. 2B is a two coordinate illustration of distributed subcarrierallocation for frequency-selective multi-user scheduling and frequencydiversity in OFDM;

FIG. 3 is an illustration of a simplified example of a 4×4 MIMO system;

FIG. 4A and FIG. 4B show an illustration of an example of pre-coding asused in a MIMO system;

FIG. 5A and FIG. 5B show an illustration of an example of receiverprocessing of pre-coding as used in a MIMO system;

FIG. 6 is an illustration of an example of phase shift applied tosubcarriers;

FIG. 7 is an illustration of cyclic delay diversity (CDD) procoding;

FIG. 8 is an illustration of precoding with a composite matrix C usedfor spatial multiplexing of four data streams in a 4×4 MIMO system;

FIG. 9 is an illustration of a transmission rank adapted spatialmultiplexing method using cyclic delay diversity (CDD) precoding;

FIG. 10 is an illustration of a method to change precoders for eachsubcarrier for the practice of the principles of the present inventions;and

FIG. 11 is an illustration of another method to change precoders eachsubcarrier or the practice of the principles of the present inventions.

DETAILED DESCRIPTION OF THE INVENTION

For easily understanding the present invention, like numbers refer tolike elements throughout this specification.

A simplified example of data transmission/reception using OrthogonalFrequency Division Multiplexing (OFDM) is shown in FIG. 1. The data tobe transmitted is modulated by a quadrature amplitude modulation (QAM)modulator 111. The QAM modulated symbols are serial-to-parallelconverted by a serial-to-parallel convertor 113 and input to an inversefast Fourier transform (IFFT) unit 115. The serial-to-parallel convertedmodulated symbols are precoded by a precoder 114. At the output of IFFTunit 115, N time-domain samples are obtained. Here N refers to thesampling number of IFFT/FFT used by the OFDM system. The signaltransmitted from IFFT unit 115 is parallel-to-serial converted by aparallel-to-serial convertor 117 and a cyclic prefix (CP) 119 is addedto the signal sequence. The resulting sequence of samples is referred toas OFDM symbol. At the receiver, the cyclic prefix is firstly removed atcyclic prefix remover 121 and the signal is serial-to-parallel convertedby parallel-to-serial 123 before feeding the converted parallel signalinto fast Fourier transform (FFT) transformer 125. The precodedmodulated symbols are decoded and recovered by a decoder 126. Output ofdecoder 126 is parallel-to-serial converted by parallel-to-serialconvertor 128 and the resulting symbols are input to the QAM demodulator129.

The total bandwidth in an OFDM system is divided into narrowbandfrequency units called subcarriers. The number of subcarriers is equalto the FFT/IFFT size N used in the system. In general, the number ofsubcarriers used for data is less than N because some subcarriers at theedge of the frequency spectrum are reserved as guard subcarriers. Ingeneral, no information is transmitted on guard subcarriers.

In a communication link, a multi-path channel results in afrequency-selective fading. Moreover, in a mobile wireless environment,the channel also results in a time-varying fading. Therefore, in awireless mobile system employing OFDM based access, the overall systemperformance and efficiency can be improved by using, in addition totime-domain scheduling, frequency-selective multi-user scheduling. In atime-varying frequency-selective mobile wireless channel, it is alsopossible to improve the reliability of the channel by spreading and/orcoding the information over the subcarriers.

FIG. 2A illustrates contiguous or localized subcarrier allocation forfrequency-selective multi-user scheduling and frequency diversity inOFDM, and FIG. 2B illustrates of distributed subcarrier allocation forfrequency-selective multi-user scheduling and frequency diversity inOFDM.

In case of frequency-selective multi-user scheduling, a contiguous setof subcarriers potentially experiencing an upfade is allocated fortransmission to a user. The total bandwidth is divided into subbandsgrouping multiple contiguous, or localized subcarriers as shown in FIG.2A where subcarriers f₁, f₂, f₃ and f₄ are grouped into a subband fortransmission to a user in frequency-selective multi-user schedulingmode. Upfade describes a situation where signal gains strength whensignals travel from the transmitting to the receiving antenna by two ormore paths.

In case of frequency-diversity transmission, the allocated subcarriersare preferably uniformly distributed over the whole spectrum as is alsoshown in FIG. 2B. The frequency-selective multi-user scheduling isgenerally beneficial for low mobility users for which the channelquality can be tracked. The channel quality can generally not be trackedfor high mobility users (particularly in a frequency-division-duplexsystem where the fading between the downlink and uplink is independent),however, due to channel quality feedback delays and hence the frequencydiversity transmission mode is preferred.

Turning now to FIG. 3, Multiple Input Multiple Output (MIMO) schemes usemultiple transmitting antennas and multiple receiving antennas toimprove the capacity and reliability of a wireless communicationchannel. A MIMO system capacity increases a function of K where K is theminimum of number of transmitting antennas (M) at transmitter andreceiving antennas (N) at receiver, i.e. K=min(M,N). A simplifiedexample of a 4×4 MIMO system is shown in FIG. 3. In this example, fourdifferent data streams Data Streams 1 to 4 are transmitted separatelyfrom the four transmitting antennas Ant1 _(T) to Ant4 _(T). Thetransmitted signals are received at the four receiving antennas Ant1_(R) to Ant4 _(R). Spatial signal processing is performed on thereceived signals in order to recover the four data streams. An exampleof spatial signal processing is V-BLAST which uses the successiveinterference cancellation principle to recover the transmitted datastreams. Other variants of MIMO schemes include schemes that performsome kind of space-time coding across the transmitting antennas (e.g.D-BLAST) and also beamforming schemes such as SDMA (Spatial Divisionmultiple Access).

The MIMO channel estimation contemplates estimating the channel gain andphase information for links from each of the transmitting antennas toeach of the receiving antennas. Therefore, the channel for M×N MIMOsystem uses an N×M matrix:

$\begin{matrix}{H = \begin{bmatrix}a_{11} & a_{12} & \ldots & a_{1M} \\a_{21} & a_{22} & \ldots & a_{2M} \\\vdots & \vdots & \ldots & \vdots \\a_{N1} & a_{M2} & \ldots & a_{NM}\end{bmatrix}} & (6)\end{matrix}$where H is the MIMO channel matrix and a_(ij) represents the channelgain from transmitting antenna j to receiving antenna i. In order toenable the estimations of the elements of the MIMO channel matrix,separate pilots are transmitted from each of the transmitting antennas.

Turning now to FIGS. 4A, 4B, an optional pre-coding scheme employs aunitary pre-coding before mapping the data streams to physical antennasas is shown in FIG. 4A and FIG. 4B. FIG. 4A shows the precoding processhappening at precoder 114 at transmitter as shown in FIG. 4B.Transmitter as shown in 4B has same structure and components as thetransmitter as shown in FIG. 1. A set of Virtual Antennas (VA) 411including VA1 and VA2 is created before the pre-coding. In this case,each of the codeword is potentially transmitted from all physicaltransmitting antennas 413 used in the superimposed informationtransmission. A virtual antenna is a virtual port created by precodingmatrix in front of the physical antennas. Symbols or signals transmittedover virtual antennas are mapped to multiple physical antennas. Twoexamples of unitary precoding matrices, P₁ and P₂ for the case of twotransmitting antennas may be:

$\begin{matrix}{{P_{1} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}},{P_{2} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}}}} & (7)\end{matrix}$

Assuming modulation symbols S₁ and S₂ are transmitted at a given timefrom stream 1 and stream 2 respectively. Then the modulation symbolsafter precoding with matrix P₁ and P₂ may be written as:

$\begin{matrix}{T_{1} = {{P_{1}\begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} = {{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}} \times \begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} = {\frac{1}{\sqrt{2}}\begin{bmatrix}{S_{1} + S_{2}} \\{S_{1} - S_{2}}\end{bmatrix}}}}} & (8) \\{T_{2} = {{P_{2}\begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} = {{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\j & {- j}\end{bmatrix}} \times \begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} = {\frac{1}{\sqrt{2}}\begin{bmatrix}{S_{1} + S_{2}} \\{{jS}_{1} - {jS}_{2}}\end{bmatrix}}}}} & (9)\end{matrix}$

Therefore, symbol

$T_{11} = {{\frac{( {S_{1} + S_{2}} )}{\sqrt{2}}\mspace{14mu}{and}\mspace{14mu} T_{12}} = \frac{( {S_{1} - S_{2}} )}{\sqrt{2}}}$will be respectively transmitted from antenna ANT1 _(T) and antenna ANT2_(T) when precoding is done by using preceding matrix P₁. Similarly,symbol

$T_{21} = {{\frac{( {S_{1} + S_{2}} )}{\sqrt{2}}\mspace{14mu}{and}\mspace{14mu} T_{22}} = \frac{( {{jS}_{1} - {jS}_{2}} )}{\sqrt{2}}}$will be respectively transmitted from antenna ANT1 _(T) and antenna ANT2_(T) when precoding is done using precoding matrix P₂ as shown in FIG.4A. It should be noted that precoding is done on an OFDM subcarrierlevel before the IFFT operation is performed by IFFT unit 115, asillustrated in FIG. 4A and FIG. 4B.

Turning now to FIG. 5A and FIG. 5B, in a pre-coded MIMO system, inverseoperations are performed at the receiver as shown in FIG. 5B to recoverthe transmitted symbols. Receiver as shown in 5B has same structure andcomponents as the receiver as shown in FIG. 1. Precoding revertingprocess as shown in FIG. 5A happens at precoding inverter 126. Thereceived symbols are multiplied with the inverse precoding matrices asgiven below.

$\begin{matrix}{{{{inv}( P_{1} )} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}},{{{inv}( P_{2} )} = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}}}} & (10)\end{matrix}$

It should be noted that the inverse of a unitary precoding matrix cansimply be obtained by taking the complex conjugate transpose of thepre-coding matrix. FIG. 5A shows the inverse precoding executed inprecoding inverter 126 as shown in FIG. 5B. The symbols transmitted byphysical transmitting antennas 413 including are decoded by multiplyingthe received symbol vector with the inverse pre-coding matrices as givenbelow.

$\begin{matrix}{{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}} \times {\frac{1}{\sqrt{2}}\begin{bmatrix}{S_{1} + S_{2}} \\{S_{1} - S_{2}}\end{bmatrix}}} = \begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} & (11) \\{{{\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {- j} \\1 & j\end{bmatrix}} \times {\frac{1}{\sqrt{2}}\begin{bmatrix}{S_{1} + S_{2}} \\{{jS}_{1} - {jS}_{2}}\end{bmatrix}}} = \begin{bmatrix}S_{1} \\S_{2}\end{bmatrix}} & (12)\end{matrix}$

In the prior art, a precoding approach is applied to both transmitdiversity and MIMO spatial multiplexing. A composite precoder isconstructed based on a unitary precoder such as Fourier matrix precodermultiplied with another unitary precoder representing a transmitdiversity scheme such as cyclic delay diversity. It should be noted thatthe principles of the current invention also applies to the cases ofnon-unitary precoding or unitary precoders other than Fourier matrixprecoder.

A Fourier matrix is a N×N square matrix with entries given by:P _(mn) =e ^(j2πmn/N) m,n=0, 1, . . . (N−1)  (13)

A 2×2 Fourier matrix can be expressed as:

$\begin{matrix}\begin{matrix}{P_{2} = \begin{bmatrix}1 & 1 \\1 & {\mathbb{e}}^{j\;\pi}\end{bmatrix}} \\{= \begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}}\end{matrix} & (14)\end{matrix}$

Similarly, a 4×4 Fourier matrix can be expressed as:

$\begin{matrix}{P_{4} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & {\mathbb{e}}^{{j\pi}/2} & {\mathbb{e}}^{j\pi} & {\mathbb{e}}^{{j3\pi}/2} \\1 & {\mathbb{e}}^{j\pi} & {\mathbb{e}}^{j2\pi} & {\mathbb{e}}^{j3\pi} \\1 & {\mathbb{e}}^{{j3\pi}/2} & {\mathbb{e}}^{j3\pi} & {\mathbb{e}}^{{j9\pi}/2}\end{bmatrix} = \begin{bmatrix}1 & 1 & 1 & 1 \\1 & j & {- 1} & {- j} \\1 & {- 1} & 1 & {- 1} \\1 & {- j} & {- 1} & j\end{bmatrix}}} & (15)\end{matrix}$

Multiple preceding matrices may be defined by introducing a shiftparameter (g/G) in the Fourier matrix as given by:

$\begin{matrix}{{P_{mn} = {{\mathbb{e}}^{{j2\pi}\;{m{({n + \frac{g}{G}})}}}m}},{n = 0},1,{\ldots\mspace{14mu}( {N - 1} )},} & (16)\end{matrix}$Here, G denotes a shift value.

A set of four 2×2 Fourier matrices can be defined by taking G=4. Thesefour 2×2 matrices with g=0, 1, 2 and 3 are written as:

$\quad\begin{matrix}{{P_{2}^{0} = {{\begin{bmatrix}1 & 1 \\1 & {- 1}\end{bmatrix}P_{2}^{1}} = \begin{bmatrix}1 & 1 \\{\mathbb{e}}^{{j\pi}/4} & {- {\mathbb{e}}^{{j\pi}/4}}\end{bmatrix}}}{P_{2}^{2} = {\begin{bmatrix}1 & 1 \\{\mathbb{e}}^{{j\pi}/2} & {\mathbb{e}}^{{j3\pi}/4}\end{bmatrix}{P_{2}^{3 =}\begin{bmatrix}1 & 1 \\{\mathbb{e}}^{{j3\pi}/4} & {- {\mathbb{e}}^{{j3\pi}/4}}\end{bmatrix}}}}} & (17)\end{matrix}$

A cyclic delay diversity scheme can be implemented in the frequencydomain with a phase shift of e^(jφ) ^(i) ^(k) applied to subcarrier ktransmitted from the ith transmitting antenna. The angle

$\begin{matrix}{\varphi_{i} = {\frac{2\pi}{N}D_{i}}} & (18)\end{matrix}$where D_(i) is the value of cyclic delay in samples applied from the ithantenna.

It should be noted that other functions can be used to derive thefrequency domain phase shift. As shown in FIG. 6, it is also possible tokeep the phase shift constant for a group of subcarriers and allowed tovary from one group of subcarriers to the next group. In FIG. 6, SB1through SB8 present eight subbands. Phase shifts Φ₁ through Φ₈ presentconstant phase shift value for SB1 through SB8 respectively. Forexample, a total phase shift is 2π for a subband and the phase shift foreach subcarrier is 2π/8. The number of subbands in FIG. 6 may be numbersother than eight.

The cyclic delay diversity can be seen as precoding with precodingmatrix D₄ as shown in equation (19) for the case of four transmittingantennas:

$\begin{matrix}{D_{4} = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & {\mathbb{e}}^{{j\phi}_{1}k} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{j\phi}_{2}k} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\phi}_{3}k}\end{bmatrix}} & (19)\end{matrix}$

FIG. 7 illustrate cyclic delay diversity (CDD) procoding. As shown inFIG. 7, symbol S1 with antenna and frequency (subcarrier) dependentphase shifts are transmitted from multiple antennas VA1-VA4. No phaseshift is applied for the symbol transmitted from the first antenna ANT1_(T). In FIG. 7, a symbol S₁ is selected as a sample symbol amongmultiple symbols to show the phase shift at different antennas. S₁ hasno phase shift at antenna ANT1 _(T), while S₁ different phase shifts atthe second antenna ANT2 _(T) through the forth antenna ANT4 _(T) bymultiplying e^(jφ) ¹ ^(k), e^(jφ) ² ^(k) and e^(jφ) ³ ^(k) respectively.

The Fourier matrix precoding may be combined with the CDD precoding togenerate a composite precoder C for the four transmitting antennas caseas below:

$\begin{matrix}\begin{matrix}{C = {{D \times P} = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & {\mathbb{e}}^{{j\phi}_{1}k} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{j\phi}_{2}k} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\phi}_{3}k}\end{bmatrix} \times \begin{bmatrix}1 & 1 & 1 & 1 \\1 & {\mathbb{e}}^{{j\pi}/2} & {\mathbb{e}}^{j\pi} & {\mathbb{e}}^{{j3\pi}/2} \\1 & {\mathbb{e}}^{j\pi} & {\mathbb{e}}^{j2\pi} & {\mathbb{e}}^{j3\pi} \\1 & {\mathbb{e}}^{{j3\pi}/2} & {\mathbb{e}}^{j3\pi} & {\mathbb{e}}^{{j9\pi}/2}\end{bmatrix}}}} \\{= \begin{bmatrix}1 & 1 & 1 & 1 \\{\mathbb{e}}^{{j\phi}_{1}k} & {\mathbb{e}}^{j{({{\pi/2} + {\phi_{1}\; k}})}} & {\mathbb{e}}^{j{({\pi + {{\phi 1}\; k}})}} & {\mathbb{e}}^{j{({{3{\pi/2}} + {\phi_{1}\; k}})}} \\{\mathbb{e}}^{{j\phi}_{2}k} & {\mathbb{e}}^{j{({\pi + {\phi_{2}\; k}})}} & {\mathbb{e}}^{j{({{2\pi} + {\phi_{2}\; k}})}} & {\mathbb{e}}^{j{({{3\pi} + {\phi_{2}\; k}})}} \\{\mathbb{e}}^{{j\phi}_{3}k} & {\mathbb{e}}^{j{({{3{\pi/2}} + {\phi_{3}\; k}})}} & {\mathbb{e}}^{j{({{3\pi} + {{\phi 3}\; k}})}} & {\mathbb{e}}^{j{({{9{\pi/2}} + {\phi_{3}k}})}}\end{bmatrix}}\end{matrix} & (20)\end{matrix}$where cyclic delay diversity precoding matrix D is matrix D₄ and Fouriermatrix P is matrix P₄ for this four transmitting antennas transmitter.

The order of matrix D and matrix P in this multiplication may beexchanged and thus resulting in a transpose of matrix C (i.e. C^(T)) asgiven in equation (21). Since a cyclic time delay (or an equivalentfrequency shift) precoding is a component of combined matrix C, thephysical antennas are delayed when matrix C is used as a precodingmatrix, and the virtual antennas are delayed when matrix C^(T) is used.When symbol S₁ is input into the precoder, the virtual antennas need tobe delayed relatively to each other in order to introduce frequencyselectivity. When a single symbol is input into the precoder, the symbolis multiplied with a weight vector w, and weight vector w should not beorthogonal to any row of precoder C. For example, when vector w isselected as [1111]^(T) which is equal to the first row of precoder C,the vector is orthogonal to the other rows. Therefore, [1111]^(T) cannotbe selected as vector w. When multiple symbols are input into theprecoder through multiple antennas respectively, each physical antennaneeds to be delayed according to the corresponding symbol since onesymbol is transmitted by one virtual antenna.

$\begin{matrix}\begin{matrix}{C^{T} = {{P \times D} = {\begin{bmatrix}1 & 1 & 1 & 1 \\1 & {\mathbb{e}}^{{j\pi}/2} & {\mathbb{e}}^{j\pi} & {\mathbb{e}}^{{j3\pi}/2} \\1 & {\mathbb{e}}^{j\pi} & {\mathbb{e}}^{j2\pi} & {\mathbb{e}}^{j3\pi} \\1 & {\mathbb{e}}^{{j3\pi}/2} & {\mathbb{e}}^{j3\pi} & {\mathbb{e}}^{{j9\pi}/2}\end{bmatrix} \times \begin{bmatrix}1 & 0 & 0 & 0 \\0 & {\mathbb{e}}^{{j\phi}_{1}k} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{j\phi}_{2}k} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\phi}_{3}k}\end{bmatrix}}}} \\{= \begin{bmatrix}1 & {\mathbb{e}}^{{j\phi}_{1}k} & {\mathbb{e}}^{{j\phi}_{2}k} & {\mathbb{e}}^{{j\phi}_{3}k} \\1 & {\mathbb{e}}^{j{({{\pi/2} + {\phi_{1}\; k}})}} & {\mathbb{e}}^{j{({\pi + {\phi_{2}\; k}})}} & {\mathbb{e}}^{j{({{3{\pi/2}} + {\phi_{3}\; k}})}} \\1 & {\mathbb{e}}^{j{({\pi + {\phi_{1}\; k}})}} & {\mathbb{e}}^{j{({{2\pi} + {\phi_{2}\; k}})}} & {\mathbb{e}}^{j{({{3\pi} + {\phi_{3}\; k}})}} \\1 & {\mathbb{e}}^{j{({{3{\pi/2}} + {\phi_{1}\; k}})}} & {\mathbb{e}}^{j{({{3\pi} + {\phi_{2}\; k}})}} & {\mathbb{e}}^{j{({{9{\pi/2}} + {\phi_{3}k}})}}\end{bmatrix}}\end{matrix} & (21)\end{matrix}$

Turing now to FIG. 8, in the case of spatial multiplexing of fourstreams in a 4×4 system, symbol column matrix S is multiplied by thecomposite preceding matrix C to get a symbol column vector T (i.e. [T₁,T₂, T₃, T₄]^(T)) transmitted from the physical antennas. FIG. 8illustrates a precoding by composite matrix C for spatial multiplexingof four streams S₁, S₂, S₃ and S₄ in a 4×4 MIMO (i.e., 4 transmittingantennas and 4 receiving antennas) system.

$\begin{matrix}{\begin{bmatrix}T_{1} \\T_{2} \\T_{3} \\T_{4}\end{bmatrix} = {{C \times S} = {\begin{bmatrix}1 & 1 & 1 & 1 \\{\mathbb{e}}^{{j\phi}_{1}k} & {\mathbb{e}}^{j{({{\pi/2} + {\phi_{1}k}})}} & {\mathbb{e}}^{j{({\pi + {{\phi 1}\; k}})}} & {\mathbb{e}}^{j{({{3{\pi/2}} + {\phi_{1}\; k}})}} \\{\mathbb{e}}^{{j\phi}_{2}k} & {\mathbb{e}}^{j{({\pi + {\phi_{2}k}})}} & {\mathbb{e}}^{j{({{2\pi} + {\phi_{2}k}})}} & {\mathbb{e}}^{j{({{3\pi} + {\phi_{2}\; k}})}} \\{\mathbb{e}}^{{j\phi}_{3}k} & {\mathbb{e}}^{j{({{3{\pi/2}} + {\phi_{3}k}})}} & {\mathbb{e}}^{j{({{3\pi} + {{\phi 3}\; k}})}} & {\mathbb{e}}^{j{({{9{\pi/2}} + {\phi_{3}\; k}})}}\end{bmatrix} \times \begin{bmatrix}S_{1} \\S_{2} \\S_{3} \\S_{4}\end{bmatrix}}}} & (22) \\{\begin{bmatrix}T_{1} \\T_{2} \\T_{3} \\T_{4}\end{bmatrix} = \begin{bmatrix}{S_{1} + S_{2} + S_{3} + S_{4}} \\{{S_{1} \cdot {\mathbb{e}}^{{j\phi}_{1}k}} + {S_{2} \cdot {\mathbb{e}}^{j{({{\pi/2} + {\phi_{1}k}})}}} + {S_{3} \cdot {\mathbb{e}}^{j{({\pi + {{\phi 1}\; k}})}}} + {S_{4} \cdot {\mathbb{e}}^{j{({{3{\pi/2}} + {\phi_{1}k}})}}}} \\{{S_{1} \cdot {\mathbb{e}}^{{j\phi}_{2}k}} + {S_{2} \cdot {\mathbb{e}}^{j{({\pi + {\phi_{2}k}})}}} + {S_{3} \cdot {\mathbb{e}}^{j{({{2\pi} + {\phi_{2}k}})}}} + {S_{4} \cdot {\mathbb{e}}^{j{({{3\pi} + {\phi_{2}k}})}}}} \\{{S_{1} \cdot {\mathbb{e}}^{{j\phi}_{3}k}} + {S_{2} \cdot {\mathbb{e}}^{j{({{3{\pi/2}} + {\phi_{3}k}})}}} + {S_{3} \cdot {\mathbb{e}}^{j{({{3\pi} + {{\phi 3}\; k}})}}} + {S_{4} \cdot {\mathbb{e}}^{j{({{9{\pi/2}} + {\phi_{3}k}})}}}}\end{bmatrix}} & (23)\end{matrix}$In the case of 2Tx antennas and (φ₁=π, and P is a DFT matrix, thecombined matrix C becomes column permutation on alternative subcarriersas follows:

$\begin{matrix}{C = {{DP}_{2} = {{\begin{bmatrix}1 & 0 \\0 & {\mathbb{e}}^{{j\phi}_{1}k}\end{bmatrix}\begin{bmatrix}1 & {- 1} \\1 & 1\end{bmatrix}} = {\begin{bmatrix}1 & {- 1} \\{\mathbb{e}}^{{j\phi}_{1}k} & {\mathbb{e}}^{{j\phi}_{1}k}\end{bmatrix}.}}}} & (24)\end{matrix}$Here, 2Tx indicates two transmitting antennas structure transmitter.In case of 4Tx antennas and with a further restriction of φ₁=π/2,φ₂=2φ₁, φ₃=3φ₁, precoding matrix C is again a column permutation matrixas follows:

$\begin{matrix}{C = {{D \times P} = \begin{bmatrix}1 & 1 & 1 & 1 \\{\mathbb{e}}^{j\frac{\pi}{2}k} & {\mathbb{e}}^{j\frac{\pi}{2}{({1 + k})}} & {\mathbb{e}}^{j\frac{\pi}{2}{({2 + k})}} & {\mathbb{e}}^{j\frac{\pi}{2}{({3 + k})}} \\{\mathbb{e}}^{{j\pi}\; k} & {\mathbb{e}}^{{j\pi}{({1 + k})}} & {\mathbb{e}}^{{j\pi}{({2 + k})}} & {\mathbb{e}}^{{j\pi}{({3 + k})}} \\{\mathbb{e}}^{j\frac{3\pi}{2}k} & {\mathbb{e}}^{j\frac{3\pi}{2}{({1 + k})}} & {\mathbb{e}}^{j\frac{3\pi}{2}{({2 + k})}} & {\mathbb{e}}^{j\frac{3\pi}{2}{({3 + k})}}\end{bmatrix}}} & (25)\end{matrix}$Here, 4Tx indicates four transmitting antennas structure transmitter.For a large-delay CDD, precoding for spatial multiplexing may be doneaccording to following equation:y(k)=D(k)Ps(k).  (26)where D(k) is a N_(t)×N_(t) matrix (N_(t) denotes the number oftransmitting antennas), P is 4×p matrix, s(k) is symbols to be precodedand y(k) is precoded symbols.Precoding CDD Structure for 2Tx and 4Tx Antennas

FIG. 9 illustrates an alternative precoding CDD structure is proposed indocuments R1-072461 and R1-072019 of “3GPP TSG-RAN WG1 #49”. In thisstructure, large-delay CDD is applied in conjunction with the precodingmatrix, if a feedback of PMI (preceding matrix indication) is available.For large-delay CDD with PMI feedback, the codebook shall be selectedfrom the single user MIMO (SU-MIMO) codebook or a subset thereof.Therefore, for large-delay CDD, precoding for spatial multiplexing shallbe done according to equation (27) as follows:y(k)=W(k)QD(k)Ps(k)  (27)where a precoding matrix W(k) is selected from the codebook having asize of N×p. Note that k is the subcarrier index, N_(t) is the number ofantenna ports and p is the transmission rank. Fourier matrix P and D(k)are of size p×p, and precoding matrix W(k) is a N_(t)×p matrix. PrecoderQ could be in several different forms, and s(k) is the symbols to beprecoded and y(k) is the precoded symbols. Two examples of Q is Q=Iwhere I is the p×p identity matrix (in this case Q can be removed), orQ=P⁻¹ which is the inverse matrix of P.

Note that the number of layers is equal to the transmission rank p incase of spatial multiplexing. Fourier matrix P may be defined asfollows:P _(mn)=exp(−j2πmn/p) for m=0, 1, . . . p−1 and n=0, 1, . . . p−1.  (28)Cyclic delay diversity precoder D(k) shall be selected from Table 1.

TABLE 1 Large-delay cyclic delay diversity with PMI feedback Number of δantenna port Transmis- Large N_(t) sion rank p D(k) delay 1 1 — — 2 1[1] 0 2 $\begin{bmatrix}1 & 0 \\0 & {\mathbb{e}}^{{- {j2}} \cdot k \cdot \delta}\end{bmatrix}\quad$ 1/2 4 1 [1] 0 2 $\begin{bmatrix}1 & 0 \\0 & {\mathbb{e}}^{{- {j2}} \cdot k \cdot \delta}\end{bmatrix}\quad$ 1/2 3 $\begin{bmatrix}1 & 0 & 0 \\0 & {\mathbb{e}}^{{- {j2}} \cdot k \cdot \delta} & 0 \\0 & 0 & {\mathbb{e}}^{{{- {j2}} \cdot k \cdot 2}\delta}\end{bmatrix}\quad$ 1/3 4 $\begin{bmatrix}1 & 0 & 0 & 0 \\0 & {\mathbb{e}}^{{- {j2}} \cdot k \cdot \delta} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{{- {j2}} \cdot k \cdot 2}\delta} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{{- {j2}} \cdot k \cdot 3}\delta}\end{bmatrix}\quad$ 1/4

FIG. 9 shows a transmission rank adapted spatial multiplexing method.Symbol s(k) having symbol vectors s₁(k) to s_(p)(k) carried by systemlayers 1 to N*p are precoded by procoding matrix W(k), Q and P. Theprecoding matrix W(k) is a channel dependent precoder which is dependentupon a feedback of PMI (preceding matrix indication). Fourier matrix Pmay be defined as follows:P _(mn)=exp(−j2πmn/p) for m=0, 1, . . . p−1 and n=0, 1, . . . p−1  (29)Precoding matrix Q may be in several different forms. Two examples of Qis Q=I where I is p×p identity matrix (in this case Q can be removed),or Q=P⁻¹ which is the inverse matrix of P. Cyclic delay diversityprecoding matrix D(k) is provided as:

$\begin{matrix}{D = {\begin{bmatrix}1 & 0 & 0 & 0 \\0 & \ddots & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{j\phi}_{p - 2}k} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{j\phi}_{p - 1}k}\end{bmatrix}.}} & (30)\end{matrix}$The precoded symbols y(k) are transformed by inverse fast Fouriertransform (IFFT) unit 115 and transmitted by transmitters ANT1 _(T) toANT4 _(T).

In this precoding CDD method, it is assumed that matrix W(k) is chosenaccording the PMI, which is obtained from uplink feedback. The uplinkfeedback refers to the feedback signal transmitted from the mobilereceiver. PMI is defined as “preceding matrix index”, and is used in the3GPP LTE RAN1 discussion to indicate the choice of the codeword within acodebook, and this choice is being feedback from the mobile to thebasestation. Once a PMI is obtained for a subband, the same choice ofpreceding matrix W(k) is applied throughout this subband. That is, W(k)maintains the same within the same subband. In high speed scenarios,however, the PMI feedback is not reliable and the PMI in the feedbackcannot be used. This system is defined as an open-loop mode. It was notclear how to select precoder W(k) in this open-loop system case. On theassumption that there is a system codebook C_(U)(P)={c₁(p), . . . ,c_(N) _(p) (p)}, the PMI feedback by the User Equipment (UE) onsubcarrier k is used to pick one code-word out of a number of N_(p)code-words, and the selection of this codeword on subcarrier k is calledprecoding matrix W(k).

In this invention, several improved methods of selecting precedingmatrix W(k) for high-speed open-loop precoding CDD are proposed forvarious antenna correlation configurations.

In one embodiment of the current invention, W(k) is selected accordingto a feedback without preceding matrix index (PMI) in the uplink foreach given UE, and this feedback is different from the dynamic PMI. SameW(k) is applied to the UE across the scheduled subband. This method isespecially useful in the configuration where the Node-B antennas arehighly correlated.

Selection Based on SU-MIMO Codebook

In another embodiment of the current invention, the SU-MIMO codebook isdenoted as C_(U)(p), for a given transmission rank p that may be 1, 2, 3or 4. The size of the codebook for rank p is denoted by N_(p). Codewordsc_(i)(p) are denoted in the code book as equation (31):C _(U)(p)={c ₁(p), . . . , c _(N) _(p) (p)}, i=1, . . . , N _(p).  (31)Note that c_(i)(p) is a G×p matrix.The codebook is predetermined in the standard in a matrix form.

Furthermore, one way of selecting preceding matrix W(k) for rank p is tocycle through the codebook C_(U)(p) as k increases. There are twooptions of how fast the precoding matrix may change. A “code book” is aset of predetermined reference data from which a precoder is selectedwhen a predetermined situation is met. A “code word” refers to each datain a code book.

FIG. 10 illustrates the first option of how fast the precoding matrixchanges. The symbol s(k) to be precoded includes symbol vectors s₁(1),s₁(2), . . . , s₁(p) (which is signal to be transmitted on the firstgroups of subcarriers), s₂(1), . . . , s₂(p), (which is signal to betransmitted on the second group of subcarriers), . . . , s_(N)(1), . . ., and s_(N)(p) (which is signal to be transmitted on N-th groupsubcarriers). Note each group comprises of p subcarriers, and there area total of N groups, and thus the total number of subcarriers isN_(sub)=N*p. Precoding matrix W(k) may change every p subcarriers withina subband. For example, transmission rank adapted symbol vectors s₁(1)to s₁(p) are precoded by the same precoding matrix W(k) which is shownas C₁, transmission rank adapted symbol vectors s₂(1) to s₂(p) areprecoded by the same precoding matrix W(k) which is C₂ (not shown inFIG. 10), and the transmission rank adapted symbol vectors s_(N)(1) tos_(N)(p) are precoded by the same procoding matrix C_(N). The precodedtransmission rank adapted symbol vectors are then processed by IFFT unitand P/S unit in their corresponding transmission ranks, are summarizedand transmitted to their corresponding transmitting antennas. Here,ANTG_(T) indicates #G transmitting antenna. Mathematically, for anysubcarrier k that satisfies 1≦k≦N_(sub) where N_(sub) is the totalnumber of subcarriers in the sub-band scheduled for the UE, precodingmatrix satisfies equation (32):

$\begin{matrix}{{W(k)} = \{ {\begin{matrix}{{c_{1}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,N_{p}} )}} = 1} \\{{c_{2}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,N_{p}} )}} = 2} \\\; & \vdots \\{{c_{N_{p}}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,N_{p}} )}} = 0}\end{matrix},} } & (32)\end{matrix}$where N_(p) is the size of codebook.

Note that “a” is a constant shift, and a typical value of “a” is 0. Alsonote that mod( ) is the modulo operation and ┌ ┐ is the ceilingoperation.

The second option is as shown in FIG. 11. The symbol s(k) to be precodedincludes symbol vectors s₁(1), s₁(2), . . . , s₁(p), s₂(1), . . . ,s₂(p), . . . , . . . , s_(N)(1), . . . , and s_(N)(p). The precodingmatrix W(k) changes every subcarrier within the subband. For example,transmission rank adapted symbol vector s₁(1) is precoded by thepreceding matrix W(k) which is shown as C₁, transmission rank adaptedsymbol vectors s₁(2) is precoded by the precoding matrix W(k) which isC₂ (not shown in FIG. 11), the transmission rank adapted symbol vectorss₁(p) is precoded by the procoding matrix C_(p), and the transmissionrank adapted symbol vectors s_(N)(P) is precoded by the procoding matrixC_(Np). The precoded transmission rank adapted symbol vectors are thenprocessed by IFFT unit and P/S unit in their corresponding transmissionranks, are summarized and transmitted to their correspondingtransmitting antennas. Here, ANTG_(T) indicates #G transmitting antenna.Mathematically, for any subcarrier k:

$\begin{matrix}{{W(k)} = \{ {\begin{matrix}{{c_{1}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},N_{p}} )}} = 1} \\{{c_{2}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},N_{p}} )}} = 2} \\\; & \vdots \\{{c_{N_{p}}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},N_{p}} )}} = 0}\end{matrix}.} } & (33)\end{matrix}$In FIGS. 10 and 11, there are a total of N*p subcarriers. In FIG. 10,the codeword changes every p subcarriers, resulting in a total ofN*p/p=N codewords; and in FIG. 11, the codeword changes everysubcarrier, resulting in a total of N*p/1=N*p codewords.

In another embodiment of the current invention, for each codebookC_(U)(P), subsets C_(U,S)(p)⊂C_(U)(p) are defined, such thatC_(U,S)(p)={c_(s,1)(p), . . . , c_(s,J) _(p) (P)} and J_(p) is the sizeof the subset (J_(p) is less than or equal to N_(p)).

Furthermore, one way of selecting the precoding matrix for W(k) is topick a subset C_(U,S)(p) for a given rank p, and then cycle through thissubset as k increases. There are two options of how fast the precodingmatrix changes. In the first option, the precoding matrix W(k) changesevery p subcarriers within the subband, or, mathematically, for anysubcarrier k that satisfies 1≦k≦N_(sub) where N_(sub) is the totalnumber of subcarriers in the sub-band scheduled for the UE. Note that“a” is a constant shift, and a typical value of “a” is 0. Also note thatmod( ) is the modulo operation and ┌ ┐ is the ceiling operation.

$\begin{matrix}{{W(k)} = \{ \begin{matrix}{{c_{s,1}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,J_{p}} )}} = 1} \\{{c_{s,2}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,J_{p}} )}} = 2} \\\; & \vdots \\{{c_{s,J_{p}}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,J_{p}} )}} = 0}\end{matrix} } & (34)\end{matrix}$

In the second option, the precoding matrix W(k) changes every subcarrierwithin the subband, or, mathematically, for any subcarrier k:

$\begin{matrix}{{W(k)} = \{ \begin{matrix}{{c_{s,1}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},J_{p}} )}} = 1} \\{{c_{s,2}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},J_{p}} )}} = 2} \\\; & \vdots \\{{c_{s,J_{p}}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},J_{p}} )}} = 0}\end{matrix} } & (35)\end{matrix}$

In another embodiment of the invention, W(k) is selected as one of thesubmatrices in the set C_(U)(p), for a given rank p. And the W(k) isfixed for all the subcarriers in the subband scheduled for the UE.

Selection Based on DFT Submatrix

In another embodiment of the present invention, a 4Tx structure systemwill be explained as an example. This embodiment, however, is notlimited to a 4Tx structure system but may be applied to NTx structuresystem (a system having a number of transmitters other than 4). A 4TxDFT matrix is defined as follows:

$\begin{matrix}{{F = {\begin{bmatrix}f_{1} & f_{2} & f_{3} & f_{4}\end{bmatrix} = {0.5*\begin{bmatrix}1 & 1 & 1 & 1 \\1 & j & {- 1} & {- j} \\1 & {- 1} & 1 & {- 1} \\1 & {- j} & {- 1} & j\end{bmatrix}}}},} & (36)\end{matrix}$Where f_(i), i=1, . . . , 4 is the i'th column of the above DFT matrix.The set of rank dependent sub-matrices C_(F)(p) is dependent on thetransmission rank p:

$\begin{matrix}\begin{matrix}{\mspace{79mu}{{C_{F}(2)} = \{ {{c_{1}(2)},{c_{2}(2)},\ldots\mspace{11mu},{c_{6}(2)}} \}}} \\{= {\{ {\lbrack {f_{1},f_{2}} \rbrack,\lbrack {f_{2},f_{3}} \rbrack,\lbrack {f_{3},f_{4}} \rbrack,\lbrack {f_{4},f_{1}} \rbrack,\lbrack {f_{1},f_{4}} \rbrack,\lbrack {f_{2},f_{4}} \rbrack} \}.}}\end{matrix} & (37) \\\begin{matrix}{{C_{F}(3)} = \{ {{c_{1}(3)},{c_{2}(3)},\ldots\mspace{11mu},{c_{6}(3)}} \}} \\{= {\{ {\begin{bmatrix}f_{1} & f_{2} & f_{3}\end{bmatrix},\begin{bmatrix}f_{2} & f_{3} & f_{4}\end{bmatrix},\begin{bmatrix}f_{3} & f_{4} & f_{1}\end{bmatrix},\begin{bmatrix}f_{4} & f_{1} & f_{2}\end{bmatrix}} \}.}}\end{matrix} & (38) \\\begin{matrix}{\mspace{79mu}{{C_{F}(4)} = \{ {c_{1}(4)} \}}} \\{= {\{ \lbrack {f_{1},f_{2},f_{3},f_{4}} \rbrack \}.}}\end{matrix} & (39)\end{matrix}$

For each set C_(F)(p), subsets C_(F,S)(p)⊂C_(F)(p) are defined, suchthat C_(F,S)(p)={c_(s,1)(p), . . . , c_(s,J) _(p) (P)} and J_(p) is thesize of the subset (J_(p) is less than or equal to the size ofC_(F)(p)). For example, one subset of the rank 2 set is

$\begin{matrix}\begin{matrix}{{C_{F,S}(2)} = \{ {{c_{s,1}(2)},{c_{s,2}(2)},\ldots\mspace{11mu},{c_{s,4}(2)}} \}} \\{= {\{ {\lbrack {f_{1},f_{2}} \rbrack,\lbrack {f_{2},f_{3}} \rbrack,\lbrack {f_{3},f_{4}} \rbrack,\lbrack {f_{4},f_{1}} \rbrack} \}.}}\end{matrix} & (40)\end{matrix}$

Furthermore, one way of selecting the precoding matrix for W(k) is topick a subset C_(F,S)(p) for a given rank p, and then cycle through thissubset as k increases. There are two options of how fast the precodingmatrix changes.

In the first option, the precoding matrix W(k) changes every psubcarriers within the subband, or, mathematically, for any subcarrier kthat satisfies 1≦k≦N_(sub) where N_(sub) is the total number ofsubcarriers in the sub-band scheduled for the UE. Note that “a” is aconstant shift, and a typical value of “a” is 0. Also note that mod( )is the modulo operation and ┌ ┐ is the ceiling operation. “s” hereindicates precoder matrix selection is among a subset of codebook. Forexample, c_(s,2)(p) is the second code word within a subset of thecodebook, this is to distinguish from c₂(p) which indicates the secondcodeword within the original codebook.

$\begin{matrix}{{W(k)} = \{ \begin{matrix}{{c_{s,1}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,J_{p}} )}} = 1} \\{{c_{s,2}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,J_{p}} )}} = 2} \\\; & \vdots \\{{c_{s,J_{p}}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,J_{p}} )}} = 0}\end{matrix} } & (41)\end{matrix}$

In the second option, the precoding matrix W(k) changes every subcarrierwithin the subband, or, mathematically, for any subcarrier k:

$\begin{matrix}{{W(k)} = \{ \begin{matrix}{{c_{s,1}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},J_{p}} )}} = 1} \\{{c_{s,2}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},J_{p}} )}} = 2} \\\; & \vdots \\{{c_{s,J_{p}}(p)},} & {{{if}\mspace{14mu}{mod}\;( {{k + a},J_{p}} )} = 0}\end{matrix} } & (42)\end{matrix}$

As an example, in case of p=2, a=0, the subset is chosen as

$\begin{matrix}\begin{matrix}{{C_{F,S}(2)} = \{ {{c_{s,1}(2)},{c_{s,2}(2)},\ldots\mspace{11mu},{c_{s,4}(2)}} \}} \\{= {\{ {\lbrack {f_{1},f_{2}} \rbrack,\lbrack {f_{2},f_{3}} \rbrack,\lbrack {f_{3},f_{4}} \rbrack,\lbrack {f_{4},f_{1}} \rbrack} \}.}}\end{matrix} & (43)\end{matrix}$

If the first option is adopted, where the precoding matrix changes everyp=2 subcarriers, the selecting of precoding matrix W(k) becomes:

$\begin{matrix}{{W(k)} = \{ \begin{matrix}{\lbrack {f_{1},f_{2}} \rbrack,} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k}{2} \rceil,4} )}} = 1} \\{\lbrack {f_{2},f_{3}} \rbrack,} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k}{2} \rceil,4} )}} = 2} \\\; & \vdots \\{\lbrack {f_{4},f_{1}} \rbrack,} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k}{2} \rceil,4} )}} = 0}\end{matrix} } & (44)\end{matrix}$

In another embodiment of the present invention, W(k) is selected as oneof the submatrices in the set C_(F)(p), for a given rank p. And the W(k)is fixed for all the subcarriers in the subband scheduled for the UE.

In another embodiment of the present invention, the preceedingembodiments mentioned above are reversible (i.e. readably decodable)with advance reception of the precoded symbols by the receiver. In otherwords, the precoded symbols may be decoded in likely methods at thereceiver. A precoded symbol may be decoded by a selected decodingmatrix, the decoding matrix is selected by cycling through a decodecode-book within a subband, and the decoding matrix may either changeevery p subcarrier or change every subcarrier within a subband. Also,the precoded symbol may be decoded by a selected decoding matrix, thedecoding matrix is selected by cycling through a subset of the decodecode-book, and the decoding matrix may either change every p subcarrieror change every subcarrier within a subband.

The precoder is a part of the eNB baseband microprocessor.

1. A method for data transmission, comprising: selecting, at theprecoder, a codeword from a predetermined codebook based on atransmission rank, wherein each codeword in the predetermined codebookis an N_(t) by p matrix, where p is the transmission rank and N_(t) isthe number of antennas, and wherein selecting the codeword comprisesselecting the codeword for the transmission rank p by cycling throughthe codebook in a designated subband scheduled for a User; generating,at the precoder, a precoding matrix based on the selected codeword;precoding, at the precoder, a plurality of symbols with the precodingmatrix; and transmitting, at an RF amplifier enabling transmissionstage, the precoded symbols.
 2. The method of claim 1, wherein eachcodeword is selected consecutively for a specified number of timescorresponding to the transmission rank.
 3. The method of claim 1,wherein selecting the codeword further comprises changing the codewordevery p number of times in the designated subband.
 4. The method ofclaim 3, wherein the codeword, W(k), is established by:${W(k)} = \{ {\begin{matrix}{{c_{1}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,N_{p}} )}} = 1} \\{{c_{2}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,N_{p}} )}} = 2} \\\; & \vdots \\{{c_{N_{p}}(p)},} & {{{if}\mspace{14mu}{{mod}( {\lceil \frac{k + a}{p} \rceil,N_{p}} )}} = 0}\end{matrix},} $ where c_(i)(p) is the i-th codeword in thecodebook, where a is a constant shift, and where the operator mod( ) isthe modulo operation and the operator ┌ ┐ is the ceiling operation. 5.The method of claim 1, wherein selecting the codeword comprises changingthe codeword every subcarrier in the designated subband.
 6. The methodof claim 5, wherein the codeword, W(k), is established by:${W(k)} = \{ {\begin{matrix}{{c_{1}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},N_{p}} )}} = 1} \\{{c_{2}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},N_{p}} )}} = 2} \\\; & \vdots \\{{c_{N_{p}}(p)},} & {{{if}\mspace{14mu}{{mod}( {{k + a},N_{p}} )}} = 0}\end{matrix}.} $
 7. The method of claim 1, wherein the codebookis a Discrete Fourier transform matrix.
 8. The method of claim 7,wherein the codebook is a 4Tx Discrete Fourier transform matrixestablished by: ${F = {\begin{bmatrix}f_{1} & f_{2} & f_{3} & f_{4}\end{bmatrix} = {0.5*\begin{bmatrix}1 & 1 & 1 & 1 \\1 & j & {- 1} & {- j} \\1 & {- 1} & 1 & {- 1} \\1 & {- j} & {- 1} & j\end{bmatrix}}}},$ where f_(i) is the i'th column of the DiscreteFourier transform matrix, and i is the number of the column.
 9. Themethod of claim 8, wherein the Discrete Fourier transform matrixcomprises sub-matrices C_(F)(p) for 4Tx established by: $\begin{matrix}\begin{matrix}{{C_{F}(2)} = \{ {{c_{1}(2)},{c_{2}(2)},\ldots\mspace{11mu},{c_{6}(2)}} \}} \\{= {\{ {\lbrack {f_{1},f_{2}} \rbrack,\lbrack {f_{2},f_{3}} \rbrack,\lbrack {f_{3},f_{4}} \rbrack,\lbrack {f_{4},f_{1}} \rbrack,\lbrack {f_{1},f_{4}} \rbrack,\lbrack {f_{2},f_{4}} \rbrack} \}.}}\end{matrix} \\\begin{matrix}{{C_{F}(3)} = \{ {{c_{1}(3)},{c_{2}(3)},\ldots\mspace{11mu},{c_{6}(3)}} \}} \\{= {\{ {\begin{bmatrix}f_{1} & f_{2} & f_{3}\end{bmatrix},\begin{bmatrix}f_{2} & f_{3} & f_{4}\end{bmatrix},\begin{bmatrix}f_{3} & f_{4} & f_{1}\end{bmatrix},\begin{bmatrix}f_{4} & f_{1} & f_{2}\end{bmatrix}} \}.}}\end{matrix} \\\begin{matrix}{{C_{F}(4)} = \{ {c_{1}(4)} \}} \\{= {\{ \lbrack {f_{1},f_{2},f_{3},f_{4}} \rbrack \}.}}\end{matrix}\end{matrix}$
 10. The method of claim 7, wherein the codebook comprisesa set of transmission rank dependent sub-matrices C_(F)(p).
 11. Themethod of claim 1, wherein the precoding matrix is generated based onthe selected codeword, a first unitary matrix, and a second unitarymatrix.
 12. The method of claim 11, wherein the first unitary matrix isa Fourier matrix and the second unitary matrix is for cyclic delaydiversity.
 13. A transmitter for transmitting data, comprising: amodulator configured to modulate data to be transmitted via thetransmitter into a plurality of modulated symbols; a precoder configuredto select a codeword from a predetermined codebook based on atransmission rank, to generate a precoding matrix based on the selectedcodeword, and to precode the modulated symbols with the precodingmatrix, wherein selecting the codeword comprises selecting a codewordprecoding matrix W(k) for transmission rank p by cycling through thecodebook with an increment of a subcarrier index in a designated subbandscheduled for a User; and an RF amplifier configured to enabletransmission of the precoded modulated symbols.
 14. The transmitter ofclaim 13, wherein each codeword in the predetermined codebook is anN_(t) by p matrix, where p is the transmission rank, and where N_(t) isa number of antennas.
 15. The transmitter of claim 13, wherein selectingthe codeword comprises cycling through a selection of each of thecodewords in the codebook, wherein each codeword is selectedconsecutively for a specified number of times corresponding to thetransmission rank.
 16. The transmitter of claim 13, wherein thepredetermined codebook is a Discrete Fourier Transform matrix codebook.17. The transmitter of claim 16, wherein the precoder is configured toselect the codeword by changing the codeword every p subcarriers in adesignated subband.
 18. The transmitter of claim 16, wherein theprecoder is configured to select the codeword by changing the codewordevery subcarrier in a designated subband.
 19. The method of claim 13,wherein the precoding matrix is generated based on the selectedcodeword, a first unitary matrix, and a second unitary matrix.
 20. Themethod of claim 19, wherein the first unitary matrix is a Fourier matrixand the second unitary matrix is for cyclic delay diversity.